Question

A Namibia firm has an obligation to pay £1,000,000 in 3 months’ time and has exported goods worth US$500,000, payment of which is also expected in 3 months’ time. It is the end of the year, when the exchange rate between the Namibian dollar and the US dollar (NamD/USD) is 16.975 and the exchange rate between the Namibian dollar and the British pound (Nam/Pound) is 19.485. The exchange rate outlook is very blurred as it is believed that the exchange rates could move either way. The following probability distributions are available for the value of the exchange rates expected to prevail at the end of the 3-months period:

NamD/USD    Probability     NamD/GBP   Probability

16.575              0.20              19.378              0.10      

16.960              0.15              19.475              0.20

17,125              0.35              19.672              0.15

17.595              0.30              19.895              0.40

                                              19.915              0.15

(e) What are the expected spot exchange rates for the United States dollar and the British Pound against the Namibian dollar?

(f) How much does the Namibian firm expect to receive from its exports?

(g) How much does the Namibian firm expect to pay for its imports?

(h) What is the probability that the Namibian dollar will appreciate against the United States dollar?

(i) What is the probability that the Namibian dollar will depreciate against the British Pound?

Answer 1

e)

Value of the exchange rates expected to prevail at the end of the 3-months period:

NamD/USD    Probability Expected NamD/GBP   Probability Expected

(a) (b) Value (a)*(b) (c) (d) Value (c)*(d)

16.575              0.20 3.315 19.378              0.10 1.9378   

16.960              0.15 2.544   19.475              0.20 3.8950

17,125              0.35 5.994 19.672              0.15 2.9508

17.595              0.30 5.279 19.895              0.40 7.9580

19.915              0.15 2.9873

17.132 19.7289

Expected spot exchange rates for the United States dollar against the Namibian dollar = 17.132 NamD/USD

Expected spot exchange rates for the British Pound against the Namibian dollar = 19.7289 NamD/GBP

f)

Namibian firm expect to receive from its exports US$500,000

Amount to be received = 5,00,000*17.132 = NamD 8,566,000

g)

Namibian firm expect to pay for its imports £1,000,000

Amount to be paid = 1,000,000*19.7289 = NamD 19,728,900

h)

Probability that the Namibian dollar will appreciate against the United States dollar = Probability that Namibian Dollar will be less than 16.975 NamD/USD = 0.2 +0.15 = 0.35

i)

Probability that the Namibian dollar will depreciate against the British Pound = Probability that Namibian Dollar will be greater than 19.485 NamD/GBP = 0.15 + 0.4 + 0.15 = 0.7